74:J MR. p. H. CARPENTER ON THE [DeC. 19, 



while the first arm-syzygy is not on the third, but on the second 

 brachial, or between the first and second. 



Group. Actinoinetra. Srd br. Sy. 2nd br. Sy. 1 — 2 br. Sy. 



('6 distichals and 3 palmars, the 



axillaries syzygies parvioirra, 



3 disticbals and 2 palmars, the 



axillaries syzygies muliiradiata. A, 



3 disticbals, the axillary a sy- 

 zygy ; and 2 palmars united by 



. syzygy B. 



2 distichals, the axillary a sy- 

 zygy ; and 2 palmars united by 



syzygy- 



II. ■{ 2 distichals and 2 palmars, the 

 axillaries syzygies. 

 2 distichals and 3 palmars, the 



axillaries syzygies. 

 '2 distichals united by syzygy ; 



2 palmars united by syzygy. 

 jjl- J 2 distichals united by syzygy; 



■ ' 2 palmars, the axillary a syzygy. 

 2 distichals united by syzygy; 



3 palmars, the axillary a syzygy. 



Now, unless Rule 3 were known, how should any one, taking the cor- 

 rected formula for Act. parvicirra (3A'D(P)^), or for Act. multi- 

 radiata C2A'1)P(P')^), know that he could only have to deal with 

 types belonging to one of the first two groups? And unless he were also 

 acquainted with Rule 7, he could not know that Group II. represents 

 a series of types that are as yet undiscovered. But within Group I. 

 the chances of error would be two to one unless Rule 5 were known, 

 according to which the third (or second) brachial is only a syzygy 

 when there are three (or two) palmars, the axillary with a syzygy. 

 There may, however, be two palmars with the axillary a syzygy, 

 and yet the first two brachials be united by syzygy, as in species A 

 of the scheme above. This exception, to which others will doubtless 

 soon be added, also shows the weakness of Prof. Bell's system, even 

 supposing the following rules to be understood ; for its formula 

 would be IDP, identical with that of another more regular species, 

 B of the above scheme, to say nothing of half a dozen other possi- 

 bilities in Groups II. and III. 



A working method of formulation, therefore, must be elastic 

 enough to deal with such anomalies as A, and indicate exactly 

 on what joint the syzygy comes in the distichals, palmars, and 

 brachials. Further, when there are no syzygies in the ray- 

 divisiona, whether throughout them all {^Ant. palmata) or in some 

 only {Act. alternans), the number of joints in each division should 

 be clearly indicated. Thus the formula 3 A'D, as understood by 

 Prof. Bell, would stand for any one of the following existing types 

 of Actinometra, apart from any number of possibilities. 

 Act. trichoj)tcra... No palmars. 1 All with a svz ffv 



«• 1 palmar (axillary) . • ' ! in the distich^ 



^ 1 P^J™^^^ and 1 axillary beyond it. \ ^^^^ ^^^ .^ ^,^^ 



Act. TtmUifida ... 2 palmars, and another similar division. / ° er axi ary. 



